Nate H

Founder. Resolve Research. Sports. Ai. Number Theory. Bio. Social. Weird. Leftist.

[atulit @atulit_gaur]

one of the strangest things about deep learning is that high-dimensional spaces behave in ways that completely break our intuition.

1. in high dimensions, almost all the volume of a sphere concentrates near its surface. weird, right?
2. randomly chosen vectors become almost perpendicular to each other as dimensionality increases.
3. in thousands of dimensions, two random vectors will typically have a cosine similarity close to zero.
4. neural networks can use these high-dimensional spaces to represent different features as directions in their activation space, without necessarily making them overlap too much.
5. but features can still interfere with each other and share dimensions. this is one reason understanding what a neural network has actually learned is so difficult.
6. gradient descent doesn’t just adjust weights. through training, it also shapes the geometry of the representations the network learns.

[Nate H @goodlck_havefun]

10^2 + 24^2 = 26^2

[Nate H @goodlck_havefun]

Long yet very fulfilling day in the city. Got to meet a bunch of very talented, inspiring people who had some wonderful insights into geometry and the state of things.

[Nate H @goodlck_havefun]

Hey my name is in there!

[Другая планета @nihilunbounded]

An authoritative account from the experts of the proof strategy and error in the three redacted papers by OpenAI, and a detailed explanation of why the proof strategy is probably irreparable as is.

https://t.co/orvuFzHljb

[Nate H @goodlck_havefun]

Wizards Defense: Is This the Same Story? https://t.co/AgzLTDiaUS

[Nate H @goodlck_havefun]

So I thought I was a smarty pants earlier today trying to make polar coordinates a vector space over ℝ with 0 = (1,0).

Ops:
(r, θ) + (r, θ) = (rr, θ+θ (mod 2π))
c * (r, θ) = rᶜ, cθ (mod 2π))

Then I realized it fails at scaling for c = 1/2 since θ = 0 and θ = 2π point to the same vector but scale to different ones.

Then I did a google and felt so silly that I just rederived ℂ*...

[Nate H @goodlck_havefun]

This episode is fantastic so far https://t.co/7vDboIk0yT #fromfirstprinciples #ffp

[Nate H @goodlck_havefun]

I’ve been known to take unorthodox and circuitous routes to achievements. But being cited in a math article before getting a degree was even a surprise.

[Pliny the Liberator 🐉󠅫󠄼󠄿󠅆󠄵󠄐󠅀󠄼󠄹󠄾󠅉󠅭 @elder_plinius]

probably nothing

[Nate H @goodlck_havefun]

Someone from Reddit found my site and signed up at the founding rate. Makes me feel really special even if its one person. I obviously upgraded him immediately to the highest tier and played Nappy Roots on repeat.

[Nate H @goodlck_havefun]

@IlinVasily29521 Hi Vasily, I'm 38 restarting my journey in formal math. I've been a Lean hobbyist, formalizing difference Galois theory while trying to teach it to myself. Would love your look if you have time. https://t.co/sR1JsxIhFU

[Nate H @goodlck_havefun]

Just for the public record. These are my projections for #nba opening night.

[Nate H @goodlck_havefun]

@nihilunbounded @AcerFur I definitely will. Because my main goal IS to understand how to measure and formalize my intuition. That’s what makes it fun. And math is domain agnostic so the same question can be asked of multiple fields, as long as you know the right question to ask.

[Nate H @goodlck_havefun]

I will say one of the neat ones. I was teaching myself Bayesian analysis with nba players doing partial pooling. I didn’t know what I was doing. I was grouping players by sub units and see if their stats tracked.

It reminded me of when I was a kid with Collatz stopping times. So I tried it and independently replicated a study by a mathematician out of Columbia in Rome. Then I had to teach myself what I did.

[Nate H @goodlck_havefun]

So I think my questions are: is it on the producers to go and formalize what they’re doing? Is individual “slop” the problem or is it the commercialization of the proverbial “slop”? I guess - as someone who has a degree of imposter syndrome and curiosity enough to formalize my intuition: I feel and see the benefit but am unsure what responsible use would look like? I’ve felt most of my output to be “slop” and so I just keep it in a folder on my comp or a GitHub repository.

[Nate H @goodlck_havefun]

As a 38 year old back in school studying math to understand things he has done and wants to do with ai - may I weigh in with a question? And not to cast judgement but to bring up the point of respecting the field where ai is being leveraged and who the onus is on to do so? And it’s an honest question in good faith.

[Nate H @goodlck_havefun]

What if determinism wasn’t a flag you turned on but it was a tile baked into silicon and bit-exact instead? 🤔 #aihardware #nvidia

[DeepSeek @deepseek_ai]

🚀 Introducing DeepInfer, our in-house inference framework, now fully open source!

Powering DeepSeek-V4.1-Flash at scale with high throughput and low latency. We’re sharing our production stack to help the community lower compute costs, reduce energy use, and make AI more affordable.

🔗 https://t.co/JGAik1kgk0

1/4

[Nate H @goodlck_havefun]

I made this repo public to save myself GitHub actions so I might as well stake claim for how off-the-wall I am. I'm entering Jane Street's ASIC emulator comp.

https://t.co/QAq93Lqyc3

This is the initial design I am planning to lock. The Readme is stale so the FPGA and logic analyzer tests aren't up yet (will be shortly) and I have some other improvements/changes/ideas for v2.

[Nate H @goodlck_havefun]

Imagine being this old and not knowing the definition of physician…poor guy.

[Ari Fleischer @AriFleischer]

He’d be arrested if he tried to treat a patient.

He’s not even allowed to write a prescription.

He’s unlicensed.

He wears a lab coat and pretends to be a doctor when he’s not one.

Just try to make an appointment with him and let me know how it goes.

[Nate H @goodlck_havefun]

@JanCBS You’re apologizing because it was against standards and not for it being a shallow, bigoted viewpoint? Okay, Jan. 🤔